Asked by TonyMaths ๐Ÿ’ฏ

How do you prove the area of a circle?

Profile picture

VERIFIED

Verified tutor tick

Peter Jones

Experienced and passionate tutor, and recent PhD recipient

This result can be proven using A-level integration. The idea is to first form the area for a small segment of a circle, with a small angle d(theta). For a very small angle this is approximately a triangle, and so it's area is (1/2) base x height. The height is the radius r, and the base is the arc length s= r*d(theta) (another result that is learnt in A-level maths). In other words, the area of this segment is: dA= (1/2) r^2 d(theta) You then integrate over the whole circle 0 < theta < 2pi to find the full area: A = (1/2) r^2 2pi = pi*r^2 and the result is proven.

Profile picture

VERIFIED

Verified tutor tick

Primisha Patel

If you need a tutor who can help achieve that higher grade then I am it!

If the object is a circle, and you know its circumference, you would divide the circumference by pi to find the diameter of the circle. Half the diameter is the radius. Square the radius and multiply by pi to find the area of the circle.

Answers from these tutors

Asked in Maths ๐Ÿ’ฏ

ASKED BY SOMERSBY

MATHS ๐Ÿ’ฏ

How do you calculate the energy rating of an appliance?

You can use this formula to estimate an appliance's energy use: (Wattage ร— Hours Used Per Day) รท 1000 = Daily Kilowatt-hour (kWh) consumption 1 kilo...

ASKED BY DIANA

MATHS ๐Ÿ’ฏ

The tax rate on Jerome Jame's $112,000 vacation home is 25 mills. The property is assessed at full value. How much will Jerome pay in taxes this year? A. $780 B. $7,800 C. $2,800 D. $28,00?

Hello Diana. The Mills rate represents a figure amount per $1000 of the assessed value of the property (mills is derived from the Latin word "milles...

ASKED BY LACEY

MATHS ๐Ÿ’ฏ

Express 540 as a product of its prime factor?

A prime number is one which does not divide into multiples of smaller numbers and are all odd numbers so not divisible by 2. For 540 you start by di...

ASKED BY LILY

MATHS ๐Ÿ’ฏ

How do you make x the subject of an equation with fractions on each side? For example: v/7x=w/?

Your question is not clear and incomplete but if you mean (v/7x) = (w/y) Easiest way is to flip both sides upside down so (7x/v) = (y/w) Multiply bo...

ASKED BY ANNA

MATHS ๐Ÿ’ฏ

How to do Pythagoras theorem?

Pythagoras theorem States that in a right angled triangle if you square the Hypotenuse c which is longest side facing the right angle (90 degrees) i...

ASKED BY JOSH

MATHS ๐Ÿ’ฏ

How do I find the area of a triangle when I only know the three side lengths?

You need to know at least one angle otherwise it is impossible

ASKED BY FAITH

MATHS ๐Ÿ’ฏ

Increase ยฃ14120 by 4%. Give your answer rounded to 2 decimal points?

4% of 14120 = 1.04x14120 = 14684.8

ASKED BY SARAH

MATHS ๐Ÿ’ฏ

How do I plot a scatter graph with two sets of dat ?

Generate a graph with x and y. Plot the one set of data then plot the other one in a different colour. I am assuming that you are comparing the two ...

ASKED BY SOPHIE

MATHS ๐Ÿ’ฏ

How do you work out what the equation of the parallel line to my=2x+3 and passes through (0,7) is?

If a line is parallel, then the equation of the parallel line will have the same gradient as the original line. In this case, the gradient of then p...

ASKED BY ANNIE

MATHS ๐Ÿ’ฏ

How do you work out perimeter?

The perimeter of a shape is essentially just the combined length of its edges, so the simplest way to work out a perimeter is to work out the length...

Find me a tutor

We take your privacy seriously. View our policy.